Post on 15-Dec-2015
An object moving in uniform circular motion is moving in a circle with a constant speed.
uniform:not changing in form or character;
remaining the same in all cases and at all times
uniform speed=constant speedspeed is how fast an object is moving
• An accelerating object is an object that has a change in velocity.
• Velocity is a vector—which has both magnitude and direction– a change in either the magnitude or the
direction (or both) means there is a change in velocity.
• For this reason, it can be said that an object moving in a circle at constant speed is indeed accelerating.
It is accelerating because the velocity is changing
directions.
An object moving in a circle experiences an acceleration.
This acceleration is directed TOWARD THE CENTER
of the circle.
For an object moving in a circle, there must be an inward force acting upon it in order to cause
its inward acceleration.
This force is called the
Centripetal Force.the word ‘centripetal’ means “center-seeking”
Newton's First Law of Motion (the Law of Inertia)
states that….
"... objects in motion tend to stay in motion with the same speed and the same direction unless acted upon by an unbalanced force."
Centripetal Force:a physical force pushing or pulling
the object towards the center of the circle.
The word "centripetal" is merely an adjective used to describe the
direction of the force. “center-seeking”
Examples of Centripetal Force
As a car makes a turn, the force of friction acting upon the turned wheels of the car provide the centripetal force
required for circular motion.
As the moon orbits the Earth, the force of gravity acting upon the
moon provides the centripetal force required for circular motion.
As a bucket of water is tied to a string and spun in a circle, the
force of tension acting upon the bucket provides the centripetal
force required for circular motion.
Newton’s Second Law states that….
• an object which experiences an acceleration must also be experiencing a net force.
• the direction of the net force always acts in the same direction as the acceleration.
The Centripetal Force causing an object to
move in a circle creates an acceleration that is
directed toward the center of the circle.
Equations to find Centripetal
Acceleration:
R
va
2
2
24
T
Ra
in otherwords
where:v is velocityR is radiusT is timeand pi is 3.14
Find the Centripetal Acceleration of a runner
running with a velocity of 8.8 m/s around a track with a radius of 25 m.
Find the Centripetal Acceleration of a car driving around an exit ramp with a velocity of
15 m/s. Assume the exit ramp has a radius of 30
m.
A dog sits 1.5 m from the center of a merry-to-round. The merry-
go-round is set in motion, and the dog’s speed is 1.5 m/s. what is
the dog’s centripetal acceleration?
A rope attaches a tire to an overhanging tree limb. A girl
swinging on the tire has a centripetal acceleration of 3.0 m/s2. If the length of the rope
is 2.1 m, what is the girl’s speed?
A race car moving along a circular track has a centripetal acceleration of 15.4 m/s2. If the car has a tangential speed of 30
m/s, what is the distance between the car and the center of
the track?